A Gallery of Ray Tracing for Geometers

5. Rotations

Other isometries of Euclidean space, such as rotation, can be effectively illustrated using animation. Consider Klein's statement “The rotations which bring one of the regular solids into coincidence with itself collectively form a group” [6, p.5]. Using a ray tracer, you can illuminate this idea in a manner not possible in the real world. You can model two copies of the solid: one stationary and the other in rotation. Figure 10 and its corresponding animation show how this approach can be used to demonstrate the five-fold rotational symmetry of the dodecahedron. As with several of the examples given above, the animation illustrates the mathematical concept with a vividness difficult to achieve in any other way.